Year 9.2 Probability Test Name: _____________ Date: ______________ Mark: /30 Section 1: Multiple Choice Shade the MOST correct answer. 1 mark each Q1 A B C D E Q2 A B C D E Q3 A B C D E Q4 A B C D E Q5 A B C D E Question 1 The probability that Joan will win her race is 0.35. What is the probability that she will not win her race? A. B. C. D. E. 0.35 0.65 0.75 75% 1 Question 3 Amy has 2 red lipsticks, 3 pink lipsticks, and 1 purple lipstick in her bag. If she randomly pulls one out, what is the probability that she will pull out a red lipstick? A. B. C. D. E. 3/6 1/2 2/6 3/5 1/3 Q6 A B C D E Q7 A B C D E Q8 A B C D E Q9 A B C D E Q10 A B C D E Question 2 What does this say? P (picking a girl’) = 6/10 A. The probability of picking a girl is 6/10 B. The probability of not picking a girl is 6/10 C. There are 6 girls D. There are 4 girls E. The probability of picking a boy is 6/10 Question 4 Which of these cards would mean the event “an ace and a club” occurs? A. B. C. D. E. Ace of Hearts Two of Diamonds Ace of Clubs Seven of Clubs An Ace of Hearts and a Seven of Clubs Questions 5-6 relate to this Venn Diagram: Question 5 How many people play footy? A. B. C. D. E. 6 14 20 18 8 Question 6 Question 7 What is the probability of picking a student who A coin is flipped and then a 3-sided dice is plays at least footy or batty? rolled. What is the probability of getting a heads and an odd number? A. 6/8 B. 10/32 A. 0/6 C. 3/4 B. 1/6 D. 5/16 C. 2/6 E. 24/32 D. 1/3 E. 2/3 Questions 8-10 relate to this two-way table: Likes Rock Dislikes Rock Total Likes Pop 7 Dislikes Pop 23 Total 18 2 20 25 25 50 30 Question 9 What is the probability of picking someone who does not like both? A. B. C. D. E. 7/50 43/50 45/50 2/50 1/25 Question 8 Which Mix would sell the best? A. B. C. D. E. Dance Pop Pop Rock Pop Pop Rock Rock Rock Pop Question 10 If a random group of 10 people were pulled out. How many people could you expect to like rock? A. B. C. D. E. 3/5 4/5 10 6/10 3 Section 2: Short Answer Question 11 (5 marks) Phil surveyed 50 people. 18 of the people he asked likes pickles. 20 of the people he asked were younger than 16. Only 5 people under 16 liked pickles. a) What number does D represent? b) What does the number in Shaded Area A mean? (1 marks) (1 mark) c) Phil is planning a party for 120 guests who are 16 or over. i. What is the probability of a guest eating pickles? d) At the party, Phil finds out that 60 of his guests eat pickles. Comment on this. (Is it more or less than expected?) ii. How many of his guest are likely to eat pickles? (2 marks) 1 mark for probability, 1 mark for number of guests (1 mark) Question 12 (2 marks) Nigel is trying to guess the answer to two True/False questions. a) Complete the tree diagram to work out the sample space (1 mark) b) What is the probability that both answers are the same? (1 mark) Question 13 (5 marks) Mary is playing a game using a full standard deck of cards without jokers. To win she needs to draw two clubs in a row. a) Draw a tree diagram of the possible outcomes for this scenario if she returns the first card before picking the next one. b) What is the probability that she will win? (1 mark) c) How many times will Mary probably need to play to win 5 times? (3 marks) 1 for structure, 1 mark for each correct pick (1 mark) Question 14 (4 marks) Here are the real numbers of Year 8s and 9s who go to Manjimup SHS and Bridgetown HS with some numbers missing. Year 8 Goes to Manji SHS 105 Goes to Bridgetown HS 44 Year 9 Total 49 Total 128 a) What is the total number of students in Years 8 and 9 at both schools? (1 mark) c) What is the probability of randomly picking a year 9 student from Manjimup SHS? (1 mark) b) What is the probability of randomly picking a student that goes to Manjimup SHS? (1 mark) d) If both years from both schools compete in a cross country, how many year 9’s from Manjimup would you expect to finish in the top 20? (1 mark) Question 15 (4 marks) Jeff has 2 Caramello Koalas, 2 Freddo Frogs, and a Kinder Surprise. He is going to give away 2 chocolates and keep the rest for himself. a) Draw a tree diagram showing the order in which he could give away the chocolates. b) What the probability that he gives away two Caramello Koala? (1 mark) c) What is the probability that he gives away a Kinder surprise second? (2 marks) 1 for each give away (1 mark) Marking Rubric 1. List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and determine probabilities for events (ACMSP225) 2. Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226) Draws two-step tree diagrams with and without replacement 15a Quality Criteria Assigns probabilities by theoretical chances for compound scenarios 13c 15b 15c Draws two-step tree diagrams with replacement 12a 13a Assigns probabilities by counting outcomes for compound scenarios MC7 12b 13b Lists possible outcomes in a sample space. MC2 MC4 Indicators Assigns probabilities of individual outcomes. MC1 MC3 Use systematic methods to list outcomes of multi-step experiments undertaken with replacement or without replacement. Identify outcomes favourable in multi-step chance experiments Uses estimates to compare data to theoretical probabilities and predict proportions 11cii 11d Uses estimates to compare data to theoretical probabilities and predict proportions MC10 14d Estimate probabilities of compound events from information in Venn diagrams MC6 11b 11ci Above Level At Level Estimate probabilities of compound events from information in two-way tables MC9 14b 14c Working Calculates relative frequencies of compound events from information in Towards Level Venn diagrams MC5 11a Calculates relative frequencies of compound events from information in two-way tables MC8 14a Calculate relative frequencies of events and estimate probabilities of compound (‘and’, ‘or’) questions in Venn diagrams and two way tables